On 1/19/2014 3:41 PM, Jason Resch wrote:

On Jan 19, 2014, at 3:31 PM, meekerdb <meeke...@verizon.net> wrote:

On 1/19/2014 9:45 AM, Bruno Marchal wrote:
But why should that imply *existence*.

It does not. Unless we believe in the axioms, which is the case for elementary arithmetic.

But what does "believe in the axioms" mean. Do we really believe we can *always* add one more? I find it doubtful. It's just a good model for most countable things. So I can believe the axioms imply the theorems and that "17 is prime" is a theorem, but I don't think that commits me to any existence in the normal sense of "THAT exists".

Axioms are a human invention which only approach the truth that was already there. Our picking some axioms to believe in changes nothing.

You seem not to appreciate that this dissipates the one essential advantage of mathematical monism: we understand mathematics (because, I say, we invent it). But if it's a mere human invention trying to model the Platonic ding and sich then PA may not be the real arithmetic. And there will have to be some magic math stuff that makes the real arithmetic really real.


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